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Rosemary Dyson
| Speaker: |
Rosemary Dyson (OCIAM, Math. Institute, University of Oxford,
UK)
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| Date: |
Wednesday June 6, 2007
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| Title: |
Mathematical
Modelling of Curtain Coating for the Paper Industry
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Abstract
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Curtain
coating is an industrial process, traditionally used to coat
photographic film, which is now being adopted by the paper industry. A
reservoir of coating mix, typically an aqueous suspension containing 20
– 70% solids and surfactants, is formed into a curtain of fluid using
either a slot or a slide. The curtain falls under gravity until it hits
the substrate or “web” to be coated, which is conveyed quickly
underneath. The coated substrate is passed through driers to evaporate
off the water and thus the finished paper is left with a solid coating.
The coater machines have vertical “edge guides”: metal blocks with
water running over them which fix the width of the curtain as it falls
(without them, the curtain is observed to “neck in” laterally).
Although this technology is well understood in the photographic
industry, the process is run at much higher speeds in paper coating,
and the fluids used have very different rheologies.
We present a simple mathematical model for the fluid flow in the
curtain, exploiting the small aspect ratio, and examine this in the
large Reynolds number limit of industrial interest. We show explicitly
that the fluid is in free fall except for close to the substrate, but
find that the fluid can not turn onto the substrate. We reconsider the
model including a bending moment in the fluid, and find this bending
moment to be negligible except in a boundary layer close to the
substrate. Thus we again have a free fall velocity away from the
substrate, but the non-zero bending moment close to the substrate
allows the curtain to “turn the corner”. Furthermore, we have assumed a
Newtonian fluid, and we also extend it to include surface tension
effects and viscoelasticity.
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